Magnetophotoluminescence measurement of the formation time of an exciton in ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As/GaAs quantum-well structures

A magnetophotoluminescence technique is adopted to study the exciton formation processes in ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As/GaAs multi-quantum-well structures, with the cyclotron periods of carriers in the quantum wells as measures of time. It is found that exciton-related photoluminescence intensities decrease with increasing external magnetic field along the growth direction. Detailed experimental and theoretical analyses revealed that the formation time of an exciton and hence the amount of carriers taking part in radiative recombination decreases with increasing magnetic field. It is found that the exciton formation time is dominated by the time during which the electron and hole move toward each other under the Coulomb force between them. Through the fitting of experimental and theoretical results, exciton formation time is directly obtained. In addition, it is found that the formation time of an exciton is a function of carrier density, and that excitons are formed after the carrier system is cooled down.